IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i9p1388-d1641624.html
   My bibliography  Save this article

Identification and Empirical Likelihood Inference in Nonlinear Regression Model with Nonignorable Nonresponse

Author

Listed:
  • Xianwen Ding

    (Department of Statistics, Jiangsu University of Technology, Changzhou 213001, China)

  • Xiaoxia Li

    (School of Mathematics and Information Technology, Yuncheng University, Yuncheng 044000, China)

Abstract

The identification of model parameters is a central challenge in the analysis of nonignorable nonresponse data. In this paper, we propose a novel penalized semiparametric likelihood method to obtain sparse estimators for a parametric nonresponse mechanism model. Based on these sparse estimators, an instrumental variable is introduced, enabling the identification of the observed likelihood. Two classes of estimating equations for the nonlinear regression model are constructed, and the empirical likelihood approach is employed to make inferences about the model parameters. The oracle properties of the sparse estimators in the nonresponse mechanism model are systematically established. Furthermore, the asymptotic normality of the maximum empirical likelihood estimators is derived. It is also shown that the empirical log-likelihood ratio functions are asymptotically weighted chi-squared distributed. Simulation studies are conducted to validate the effectiveness of the proposed estimation procedure. Finally, the practical utility of our approach is demonstrated through the analysis of ACTG 175 data.

Suggested Citation

  • Xianwen Ding & Xiaoxia Li, 2025. "Identification and Empirical Likelihood Inference in Nonlinear Regression Model with Nonignorable Nonresponse," Mathematics, MDPI, vol. 13(9), pages 1-26, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1388-:d:1641624
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/9/1388/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/9/1388/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tianqing Liu & Xiaohui Yuan, 2020. "Doubly robust augmented-estimating-equations estimation with nonignorable nonresponse data," Statistical Papers, Springer, vol. 61(6), pages 2241-2270, December.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    3. Kenji Beppu & Kosuke Morikawa, 2024. "Verifiable identification condition for nonignorable nonresponse data with categorical instrumental variables," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 8(1), pages 40-50, January.
    4. Wang Miao & Eric J. Tchetgen Tchetgen, 2016. "On varieties of doubly robust estimators under missingness not at random with a shadow variable," Biometrika, Biometrika Trust, vol. 103(2), pages 475-482.
    5. Jiang, Depeng & Zhao, Puying & Tang, Niansheng, 2016. "A propensity score adjustment method for regression models with nonignorable missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 98-119.
    6. Zonghui Hu & Dean A. Follmann & Jing Qin, 2010. "Semiparametric dimension reduction estimation for mean response with missing data," Biometrika, Biometrika Trust, vol. 97(2), pages 305-319.
    7. Sima Sharghi & Kevin Stoll & Wei Ning, 2024. "Statistical inferences for missing response problems based on modified empirical likelihood," Statistical Papers, Springer, vol. 65(7), pages 4079-4120, September.
    8. Zhou, Yong & Wan, Alan T. K & Wang, Xiaojing, 2008. "Estimating Equations Inference With Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1187-1199.
    9. Peisong Han, 2014. "Multiply Robust Estimation in Regression Analysis With Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1159-1173, September.
    10. Liugen Xue & Junshan Xie, 2024. "Efficient robust estimation for single-index mixed effects models with missing observations," Statistical Papers, Springer, vol. 65(2), pages 827-864, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bian, Yuan & Yi, Grace Y. & He, Wenqing, 2024. "A unified framework of analyzing missing data and variable selection using regularized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    2. Zhuoer Sun & Suojin Wang, 2019. "Semiparametric estimation in regression with missing covariates using single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1201-1232, October.
    3. Lei Wang & Wei Ma, 2021. "Improved empirical likelihood inference and variable selection for generalized linear models with longitudinal nonignorable dropouts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 623-647, June.
    4. Tang, Niansheng & Xia, Linli & Yan, Xiaodong, 2019. "Feature screening in ultrahigh-dimensional partially linear models with missing responses at random," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 208-227.
    5. Xiong, Wei & Wang, Dehui & Deng, Dianliang & Wang, Xinyang & Zhang, Wanying, 2022. "Penalized multiply robust estimation in high-order autoregressive processes with missing explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    6. Liu, Tianqing & Yuan, Xiaohui & Sun, Jianguo, 2021. "Weighted rank estimation for nonparametric transformation models with nonignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    7. Puying Zhao & Hui Zhao & Niansheng Tang & Zhaohai Li, 2017. "Weighted composite quantile regression analysis for nonignorable missing data using nonresponse instrument," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 189-212, April.
    8. Shonosuke Sugasawa & Kosuke Morikawa & Keisuke Takahata, 2022. "Bayesian semiparametric modeling of response mechanism for nonignorable missing data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 101-117, March.
    9. Tianqing Liu & Xiaohui Yuan, 2020. "Doubly robust augmented-estimating-equations estimation with nonignorable nonresponse data," Statistical Papers, Springer, vol. 61(6), pages 2241-2270, December.
    10. Lu, Wenqi & Qin, Guoyou & Zhu, Zhongyi & Tu, Dongsheng, 2021. "Multiply robust subgroup identification for longitudinal data with dropouts via median regression," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    11. Xianwen Ding & Jiandong Chen & Xueping Chen, 2020. "Regularized quantile regression for ultrahigh-dimensional data with nonignorable missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(5), pages 545-568, July.
    12. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    13. Guan, Wei & Gray, Alexander, 2013. "Sparse high-dimensional fractional-norm support vector machine via DC programming," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 136-148.
    14. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    15. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
    16. Xu, Yang & Zhao, Shishun & Hu, Tao & Sun, Jianguo, 2021. "Variable selection for generalized odds rate mixture cure models with interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    17. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Emmanouil Androulakis & Christos Koukouvinos & Kalliopi Mylona & Filia Vonta, 2010. "A real survival analysis application via variable selection methods for Cox's proportional hazards model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(8), pages 1399-1406.
    19. Meng An & Haixiang Zhang, 2023. "High-Dimensional Mediation Analysis for Time-to-Event Outcomes with Additive Hazards Model," Mathematics, MDPI, vol. 11(24), pages 1-11, December.
    20. Singh, Rakhi & Stufken, John, 2024. "Factor selection in screening experiments by aggregation over random models," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1388-:d:1641624. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.